Question

A signal of 5kHz frequency is amplitude modulated on a carrier wave of frequency 2MHz. What are the frequencies of the side bands produced?

Answer 1

The frequencies of the side bands are 1.995MHz(lower side band) and 2.005MHz(upper side band).

#Consider a message signal m(t), a function in terms of time with frequency = fm. And a carrier wave c(t) with frequency fc.

#during the process of amplitude modulation, amplitude of carrier wave is changed based on the instantaneous amplitude of the message signal.

#The message signal and the carrier signal are multiplied to get an amplitude modulated signal, which is represented by s(t).

# Fourier transform is done to convert time domain signals into frequency domain signals.

# when Fourier transform is applied on s(t), S(w) is obtained which is in terms of frequency (w=2πf, f is frequency) as shown in the given image.

#Thus, frequency of upper side band is fc+fm i.e frequency of carrier wave + frequency of message signal

2000000+5000 = 2.005MHz

# frequency of lower side band is fc-fm i.e frequency of carrier wave - frequency of message signal

2000000-5000 = 1.995MHz